Dynamic-Domain RRTs: Efficient Exploration by Controlling the Sampling Domain

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Dynamic-Domain RRTs Efficient Exploration by
Controlling the Sampling Domain

• Anna Yershova1 Léonard Jaillet2 Thierry
  Siméon2 Steven M. LaValle1

1Department of Computer Science University of
Illinois Urbana, IL 61801 USA yershova,
lavalle_at_uiuc.edu
2LAAS-CNRS 7, Avenue du Colonel Roche 31077
Toulouse Cedex 04,France ljaillet, nic_at_laas.fr
Thanks to US National Science Foundation,
UIUC/CNRS funding, Kineo
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Rapidly-exploring Random Trees (RRTs)

• Introduced by LaValle and Kuffner, ICRA 1999.
• Applied, adapted, and extended in many works
  Frazzoli, Dahleh, Feron, 2000 Toussaint, Basar,
  Bullo, 2000 Vallejo, Jones, Amato, 2000 Strady,
  Laumond, 2000 Mayeux, Simeon, 2000 Karatas,
  Bullo, 2001 Li, Chang, 2001 Kuffner, Nishiwaki,
  Kagami, Inaba, Inoue, 2000, 2001 Williams, Kim,
  Hofbaur, How, Kennell, Loy, Ragno, Stedl,
  Walcott, 2001 Carpin, Pagello, 2002 Branicky,
  Curtiss, 2002 Cortes, Simeon, 2004 Urmson,
  Simmons, 2003 Yamane, Kuffner, Hodgins, 2004
  Strandberg, 2004 ...
• Also, applications to biology, computational
  geography, verification, virtual prototyping,
  architecture, solar sailing, computer graphics,
  ...

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The RRT Construction Algorithm

• GENERATE_RRT(xinit, K, ?t)
• T.init(xinit)
• For k 1 to K do
• xrand ? RANDOM_STATE()
• xnear ? NEAREST_NEIGHBOR(xrand, T)
• if CONNECT(T, xrand, xnear, xnew)
• T.add_vertex(xnew)
• T.add_edge(xnear, xnew, u)
• Return T

xnear
xnew
xinit
The result is a tree rooted at xinit
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A Rapidly-exploring Random Tree (RRT)
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Voronoi Biased Exploration
Is this always a good idea?
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Voronoi Diagram in R 2
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Voronoi Diagram in R 2
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Voronoi Diagram in R 2
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Refinement vs. Expansion
refinement
expansion
Where will the random sample fall? How to control
the behavior of RRT?
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Limit Case Pure Expansion

• Let X be an n-dimensonal ball,
• in which r is very large.
• The RRT will explore n 1 opposite directions.
• The principle directions are vertices of a
  regular (n 1)-simplex

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Determining the Boundary
Expansion dominates
Balanced refinement and expansion
The tradeoff depends on the size of the bounding
box
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Controlling the Voronoi Bias

• Refinement is good when multiresolution search is
  needed
• Expansion is good when the tree can grow and not
  blocked by obstacles
• Main motivation
• Voronoi bias does not take into account obstacles
• How to incorporate the obstacles into Voronoi
  bias?

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Bug Trap
Small Bounding Box
Large Bounding Box

• Which one will perform better?

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Voronoi Bias for the Original RRT
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Visibility-Based Clipping of the Voronoi Regions
Nice idea, but how can this be done in
practice? Even better Voronoi diagram for
obstacle-based metric
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A Boundary Node

• (a) Regular RRT, unbounded Voronoi region
• (b) Visibility region
• (c) Dynamic domain

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A Non-Boundary Node

• (a) Regular RRT, unbounded Voronoi region
• (b) Visibility region
• (c) Dynamic domain

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Dynamic-Domain RRT Bias
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Dynamic-Domain RRT Construction
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Dynamic-Domain RRT Bias
Tradeoff between nearest neighbor calls and
collision detection calls
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Experiments

• Implementation details
• MOVE3D (LAAS/CNRS)
• 333 Mhz Sunblade 100 with SunOs 5.9 (not very
  fast)
• Compiler GCC 3.3
• Fast nearest neighbor searching (Yershova
  Atramentov, LaValle, 2002)
• Two kinds of experiments
• Controlled experiments for toy problems
• Challenging benchmarks from industry and biology

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Shrinking Bug Trap
Large Medium
Small
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Shrinking Bug Trap
The smaller the bug trap, the better the
improvement
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Wiper Motor (courtesy of KINEO)

• 6 dof problem
• CD calls are expensive

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Molecule

• 68 dof problem was solved in 2 minutes
• 330 dof in 1 hour
• 6 dof in 1 min. 30 times improvement comparing to
  RRT

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Labyrinth

• 3 dof problem
• CD calls are not expensive

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Conclusions

• Controlling Voronoi bias is important in RRTs.
• Provides dramatic performance improvements on
  some problems.
• Does not incur much penalty for unsuitable
  problems.
• Work in Progress
• There is a radius parameter. Adaptive tuning is
  possible.(Jaillet et.al. 2005. Submitted to IROS
  2005)
• Application to planning under differential
  constraints.
• Application to planning for closed chains.